Circular Arc Representation based on Parametric Complex Functions

DOI

10.2991/lemcs-14.2014.107How to use a DOI?

Keywords

CNC; Circular arc; Möbius transformation

Abstract

In CNC machinery, the industrial products and machinery parts are often represented by circular arcs. A new method for representing circular arc based on parametric complex functions is presented in the paper. Since cross ratio is an invariant of the group of all Möbius transformations, and a Möbius transformation maps a circle into another circle, we represent a segment of circular arc with a parametric complex rational function. The representation has no weight factors or control parameters, and it is geometric and affine invariant. Compared with the classical method for representing circular arc, such as NURBS or C-curves, the presented method is much simpler.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Xuexiang Li
AU  - Junxiao Xue
PY  - 2014/05
DA  - 2014/05
TI  - Circular Arc Representation based on Parametric Complex Functions
BT  - Proceedings of the International Conference on Logistics, Engineering, Management and Computer Science
PB  - Atlantis Press
SP  - 462
EP  - 465
SN  - 1951-6851
UR  - https://doi.org/10.2991/lemcs-14.2014.107
DO  - 10.2991/lemcs-14.2014.107
ID  - Li2014/05
ER  -